Certainly immediately after the rapture, the whole word will be in chaos which will result in a huge mess and the deaths of many unbelievers as well. Have you seen reference to this in scripture? I can’t help but think 1 Thes 5:3 may be referring to this time period. It seems like the epitome of “sudden destruction”!
The context of 1 Thes. 5:3 is the “Day of the Lord” and says that while people are saying “peace and safety” destruction will come on them suddenly . Just after the Battle of Ezekiel 38 when the anti-Christ first comes to power there will be a brief period during which it will look like peace has come to the world. Daniel 8:25 says the anti-Christ will deceive many by means of peace.
As you know I believe the Church will have disappeared just before this Battle. While there will be great turmoil after the rapture, I think Paul was referring to the early stages of the anti-Christ’s reign. This period of time is described in Rev. 6:1-4 in the shift from the first seal to the second one.
As far as I can tell the Bible doesn’t identify conditions on Earth that specifically result from the Rapture.